'Annoyed' might be a bit harsh. Raising a bilingual child does bring some challenges that could be avoided by sticking to one language. And while his logic is flawed, it's not unreasonable to assume that learning two languages must be harder than learning one, and therefore will cause your child problems.
It's not at all unreasonable to want to raise multi-lingual kids, but I can get why he might feel a bit daunted on top of everything else that comes with parenting. Perhaps steering him in the direction of other people's experience (maybe not from a MN thread) and talking through strategies will help to reassure him. And you can talk up how it's important that your child has a grounding in both cultures - you might have no plans to relocate to Italy, but the child might like the idea later in life (or circumstances might change your plans). You don't need to threaten about 'what if we had to move to Italy and our child couldn't speak a word of it', but highlighting the extra flexibility your (extended) family would gain is worthwhile.
I've some experience of a bilingual upbringing: DD is three and speaks her second language as well as her English. We've basically gone OPOL, with me doing the English and her mum doing the other (won't specify in case of outing). So far, it's working. She doesn't have problems speaking the 'wrong' language to people (she knows, for example, that granddad only speaks English); she doesn't have problems mixing the two languages (even though they are grammatically v different and have relatively little common vocab). And she seemed to start speaking at the same age as everyone else, maybe even a little before. Even though the languages in question use different alphabets, so far there's no sign that she's muddling those either. She is just beginning to learn to read and write, but our problems are simply not recognizing the shape, rather than thinking it's a shape from language 'A' when it's really from language 'B'. I've been amazed, and humbled, by how well she's picked up the two.
I suspect he's worried that it will be a lot of work, and mostly for him because he's the native speaker and can provide the most appropriate model to imitate. In reality, I'm not sure how true that is. Teaching kids to talk involves a lot of time chattering away about anything and nothing but he'll be doing that in one language anyway - why not in his native language? There may come a point when the child needs some formal teaching; I can see that being an issue at school age when there's a structured approach to developing English-language skills and (possibly) nothing comparable in Italian. But the child will be learning the same letters, making similar sounds; worst case would be speaking Italian with an unusual British accent.
The only thing that is likely to be harder is sourcing bedtime stories, DVDs etc in Italian. I'd assume family can help with that, though, if they can send things from Italy. YouTube is also pretty handy when you need an authentic, non-Disneyfied Pinocchio.
TL;DR - it feels hard until you start doing it (like everything in parenting); it gets much easier once you start (unlike almost everything else!).